Option pricing in a regime-switching model using the fast Fourier transform

Option pricing in a regime-switching model using the fast Fourier transform

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Article ID: iaor20084527
Country: United States
Volume: 2006
Issue: 18109
Start Page Number: 1
End Page Number: 22
Publication Date: Jan 2006
Journal: Journal of Applied Mathematics and Stochastic Analysis
Authors: , ,
Keywords: markov processes, stochastic processes
Abstract:

This paper is concerned with fast Fourier transform (FFT) approach to option valuation, where the underlying asset price is governed by a regime-switching geometric Brownian motion. An FFT method for the regime-switching model is developed first. Aiming at reducing computational complexity, a near-optimal FFT scheme is proposed when the modulating Markov chain has a large state space. To test the FFT method, a novel semi-Monte Carlo simulation algorithm is developed. This method takes advantage of the observation that the option value for a given sample path of the underlying Markov chain can be calculated using the Black–Scholes formula. Finally, numerical results are reported.

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